2. Which of the following are groups? For those which are not groups, explain why not (it is enough to find one axiom that fails). For those which are, state the identity and inverses: (i) Q under x, (ii) {q Q:q> 0} under ×, (iii) {q Q:q>0} under division, (iv) {1, 2, 3, 4, 5, 6, 7} under x mod 8, (v) {1,3,5, 7) under × mod 8, (vi) {2, 4, 6, 8, 10, 12} under x mod 14, a -b b a (vii) 2 x 2 real matrices of the form both 0, (viii) The set {0,1,2,3,4,5} under the operation roy = |x+y - 5. under matrix multiplication, with a and b not

Hello there! Can you please help me out with this problem with a Cayley table? Write neatly and thank you!

Find all group homomorphisms from Z₂ XZ₁ to Z₂ XZ₁ 3 4 2 3 Find all group homomorphisms from 7/3 X 7/4 to 1/₂ X 1/3

The factor group U(16)/(9)has an element of order 4. True of false? True O Falsc